JEE Main - Types of matrices Online Test (MCQ Quiz)

1. A matrix in which all the elements are zero is called a:

A) Scalar matrix B) Null matrix C) Unit matrix D) Diagonal matrix

2. A matrix where the number of rows is equal to the number of columns is known as a:

A) Row matrix B) Column matrix C) Square matrix D) Rectangular matrix

3. Which type of matrix has only one row?

A) Column matrix B) Row matrix C) Square matrix D) Null matrix

4. A matrix with only one column is called a:

A) Row matrix B) Column matrix C) Scalar matrix D) Diagonal matrix

5. A square matrix where all the non-diagonal elements are zero is termed as a:

A) Scalar matrix B) Unit matrix C) Diagonal matrix D) Upper triangular matrix

6. In a diagonal matrix, the elements a_ij are zero when:

A) i = j B) i ≠ j C) i + j = 0 D) i < j

7. A square matrix where all the elements are identical and non-zero is a:

A) Diagonal matrix B) Unit matrix C) Scalar matrix D) Null matrix

8. A scalar matrix where the diagonal elements are all 1 is called a:

A) Null matrix B) Identity matrix C) Diagonal matrix D) Upper triangular matrix

9. An identity matrix is always a:

A) Rectangular matrix B) Row matrix C) Column matrix D) Square matrix

10. A matrix where all the elements below the main diagonal are zero is a:

A) Lower triangular matrix B) Upper triangular matrix C) Diagonal matrix D) Scalar matrix

11. In an upper triangular matrix, the elements a_ij are zero when:

A) i = j B) i > j C) i < j D) i + j = n

12. A matrix where all the elements above the main diagonal are zero is a:

A) Upper triangular matrix B) Lower triangular matrix C) Diagonal matrix D) Unit matrix

13. In a lower triangular matrix, the elements a_ij are zero when:

A) i = j B) i < j C) i > j D) i + j = n + 1

14. A triangular matrix is also a diagonal matrix if:

A) All its non-diagonal elements are zero B) All its diagonal elements are zero C) It has only one row D) It has only one column

15. A square matrix is called skew-symmetric if its transpose is equal to:

A) The matrix itself B) The negative of the matrix C) The inverse of the matrix D) The null matrix

16. For a skew-symmetric matrix A, the diagonal elements must be:

A) 1 B) Non-zero C) Zero D) Any real number

17. If A is a skew-symmetric matrix, then A^T = ?

A) A B) -A C) A⁻¹ D) 0

18. A square matrix is called symmetric if its transpose is equal to:

A) The negative of the matrix B) The null matrix C) The matrix itself D) The inverse of the matrix

19. For a symmetric matrix A, the elements satisfy the condition:

A) a_ij = -a_ji B) a_ij = a_ji C) a_ij = 0 for i ≠ j D) a_ij = 1 for i = j

20. If A is a symmetric matrix, then A^T = ?

A) -A B) A⁻¹ C) A D) 0

21. Which of the following is NOT a type of square matrix?

A) Diagonal matrix B) Row matrix C) Identity matrix D) Scalar matrix

22. A matrix of order m x n is rectangular if:

A) m = n B) m ≠ n C) m = 1 D) n = 1

23. A matrix where all elements are equal is called a:

A) Null matrix B) Scalar matrix C) Unit matrix D) Constant matrix

24. Which type of matrix has all diagonal elements equal and all non-diagonal elements zero?

A) Unit matrix B) Scalar matrix C) Identity matrix D) Diagonal matrix

25. A matrix A is orthogonal if:

A) A^T = A B) A^T = -A C) A^T A = I D) A = 0

26. If A is an orthogonal matrix, then A⁻¹ is equal to:

A) A B) -A C) A^T D) 0

27. What is the order of a null matrix if it is also a square matrix?

A) 1x1 B) nx1 C) 1xn D) nxn

28. A matrix that remains unchanged after transposition is:

A) Skew-symmetric matrix B) Symmetric matrix C) Orthogonal matrix D) Null matrix

29. A matrix that becomes its negative after transposition is:

A) Symmetric matrix B) Skew-symmetric matrix C) Identity matrix D) Scalar matrix

30. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The symmetric part is given by:

A) (A - A^T)/2 B) (A + A^T)/2 C) (A^T - A)/2 D) A + A^T

31. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The skew-symmetric part is given by:

A) (A + A^T)/2 B) (A - A^T)/2 C) (A^T + A)/2 D) A - A^T

32. A square matrix A is called periodic if A^k = I for some positive integer k. If k=1, then A is:

A) Null matrix B) Identity matrix C) Scalar matrix D) Zero matrix

33. A matrix A is idempotent if A² = A. Which of the following is an idempotent matrix?

A) Identity matrix B) Null matrix C) Both Identity and Null matrix D) Scalar matrix

34. A matrix A is involutory if A² = I. Which of the following is an involutory matrix?

A) Identity matrix B) Null matrix C) Scalar matrix D) Diagonal matrix

35. A matrix where all the elements are positive is called a:

A) Positive matrix B) Negative matrix C) Zero matrix D) Unit matrix

36. A matrix where all the elements are negative is called a:

A) Negative matrix B) Positive matrix C) Null matrix D) Diagonal matrix

37. A matrix where at least one element is non-zero is called a:

A) Null matrix B) Non-zero matrix C) Scalar matrix D) Unit matrix

38. A matrix of order 1x1 is always a:

A) Row matrix B) Column matrix C) Both Row and Column matrix D) Square matrix

39. Which type of matrix is both upper triangular and lower triangular?

A) Scalar matrix B) Unit matrix C) Diagonal matrix D) Null matrix

40. A square matrix A is called nilpotent of index k if A^k = 0 and A^(k-1) ≠ 0. If k=1, then A is:

A) Identity matrix B) Null matrix C) Scalar matrix D) Symmetric matrix

41. If A = [[2, 0], [0, 3]], this is an example of a:

A) Scalar matrix B) Unit matrix C) Diagonal matrix D) Null matrix

42. If A = [[5, 0], [0, 5]], this is an example of a:

A) Diagonal matrix B) Unit matrix C) Scalar matrix D) Identity matrix

43. If A = [[1, 0], [0, 1]], this is an example of a:

A) Scalar matrix B) Diagonal matrix C) Identity matrix D) All of the above

44. If A = [[0, 0], [0, 0]], this is an example of a:

A) Null matrix B) Identity matrix C) Scalar matrix D) Diagonal matrix

45. If A = [[1, 2], [3, 4]], this is an example of a:

A) Upper triangular matrix B) Lower triangular matrix C) Diagonal matrix D) Rectangular matrix

46. If A = [[1, 2], [0, 3]], this is an example of a:

A) Lower triangular matrix B) Upper triangular matrix C) Diagonal matrix D) Null matrix

47. If A = [[1, 0], [2, 3]], this is an example of a:

A) Upper triangular matrix B) Lower triangular matrix C) Diagonal matrix D) Scalar matrix

48. A matrix A is called skew-Hermitian if A^θ = -A, where A^θ is the conjugate transpose of A. For a real matrix to be skew-Hermitian, it must be:

A) Symmetric B) Skew-symmetric C) Diagonal D) Orthogonal

49. A matrix A is called Hermitian if A^θ = A. For a real matrix to be Hermitian, it must be:

A) Skew-symmetric B) Symmetric C) Diagonal D) Null

50. The identity matrix of order 2x2 is denoted by:

A) I₂ B) J₂ C) O₂ D) A₂

Types of matrices - Online Test

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